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PolygonsSet (Commons Math 3.2 API)
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org.apache.commons.math3.geometry.euclidean.twod</FONT>
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Class PolygonsSet</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../../../resources/inherit.gif" ALT="extended by "><A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="class in org.apache.commons.math3.geometry.partitioning">org.apache.commons.math3.geometry.partitioning.AbstractRegion</A>&lt;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Euclidean2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Euclidean2D</A>,<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/oned/Euclidean1D.html" title="class in org.apache.commons.math3.geometry.euclidean.oned">Euclidean1D</A>&gt;
      <IMG SRC="../../../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.geometry.euclidean.twod.PolygonsSet</B>
</PRE>
<DL>
<DT><B>All Implemented Interfaces:</B> <DD><A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Euclidean2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Euclidean2D</A>&gt;</DD>
</DL>
<HR>
<DL>
<DT><PRE>public class <B>PolygonsSet</B><DT>extends <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="class in org.apache.commons.math3.geometry.partitioning">AbstractRegion</A>&lt;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Euclidean2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Euclidean2D</A>,<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/oned/Euclidean1D.html" title="class in org.apache.commons.math3.geometry.euclidean.oned">Euclidean1D</A>&gt;</DL>
</PRE>

<P>
This class represents a 2D region: a set of polygons.
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>3.0</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: PolygonsSet.java 1422195 2012-12-15 06:45:18Z psteitz $</DD>
</DL>
<HR>

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&nbsp;<A NAME="nested_classes_inherited_from_class_org.apache.commons.math3.geometry.partitioning.Region"><!-- --></A>
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<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Nested classes/interfaces inherited from interface org.apache.commons.math3.geometry.partitioning.<A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/Region.Location.html" title="enum in org.apache.commons.math3.geometry.partitioning">Region.Location</A></CODE></TD>
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&nbsp;

<!-- ======== CONSTRUCTOR SUMMARY ======== -->

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<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/PolygonsSet.html#PolygonsSet()">PolygonsSet</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a polygons set representing the whole real line.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/PolygonsSet.html#PolygonsSet(org.apache.commons.math3.geometry.partitioning.BSPTree)">PolygonsSet</A></B>(<A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/BSPTree.html" title="class in org.apache.commons.math3.geometry.partitioning">BSPTree</A>&lt;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Euclidean2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Euclidean2D</A>&gt;&nbsp;tree)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a polygons set from a BSP tree.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/PolygonsSet.html#PolygonsSet(java.util.Collection)">PolygonsSet</A></B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</A>&lt;<A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/SubHyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning">SubHyperplane</A>&lt;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Euclidean2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Euclidean2D</A>&gt;&gt;&nbsp;boundary)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a polygons set from a Boundary REPresentation (B-rep).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/PolygonsSet.html#PolygonsSet(double, double, double, double)">PolygonsSet</A></B>(double&nbsp;xMin,
            double&nbsp;xMax,
            double&nbsp;yMin,
            double&nbsp;yMax)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a parallellepipedic box.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/PolygonsSet.html#PolygonsSet(double, org.apache.commons.math3.geometry.euclidean.twod.Vector2D...)">PolygonsSet</A></B>(double&nbsp;hyperplaneThickness,
            <A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Vector2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Vector2D</A>...&nbsp;vertices)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a polygon from a simple list of vertices.</TD>
</TR>
</TABLE>
&nbsp;
<!-- ========== METHOD SUMMARY =========== -->

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<B>Method Summary</B></FONT></TH>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/PolygonsSet.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">PolygonsSet</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/PolygonsSet.html#buildNew(org.apache.commons.math3.geometry.partitioning.BSPTree)">buildNew</A></B>(<A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/BSPTree.html" title="class in org.apache.commons.math3.geometry.partitioning">BSPTree</A>&lt;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Euclidean2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Euclidean2D</A>&gt;&nbsp;tree)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a region using the instance as a prototype.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/PolygonsSet.html#computeGeometricalProperties()">computeGeometricalProperties</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute some geometrical properties.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Vector2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Vector2D</A>[][]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/PolygonsSet.html#getVertices()">getVertices</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the vertices of the polygon.</TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_org.apache.commons.math3.geometry.partitioning.AbstractRegion"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from class org.apache.commons.math3.geometry.partitioning.<A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="class in org.apache.commons.math3.geometry.partitioning">AbstractRegion</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#applyTransform(org.apache.commons.math3.geometry.partitioning.Transform)">applyTransform</A>, <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#checkPoint(org.apache.commons.math3.geometry.partitioning.BSPTree, org.apache.commons.math3.geometry.Vector)">checkPoint</A>, <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#checkPoint(org.apache.commons.math3.geometry.Vector)">checkPoint</A>, <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#contains(org.apache.commons.math3.geometry.partitioning.Region)">contains</A>, <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#copySelf()">copySelf</A>, <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#getBarycenter()">getBarycenter</A>, <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#getBoundarySize()">getBoundarySize</A>, <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#getSize()">getSize</A>, <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#getTree(boolean)">getTree</A>, <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#intersection(org.apache.commons.math3.geometry.partitioning.SubHyperplane)">intersection</A>, <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#isEmpty()">isEmpty</A>, <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#isEmpty(org.apache.commons.math3.geometry.partitioning.BSPTree)">isEmpty</A>, <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#setBarycenter(org.apache.commons.math3.geometry.Vector)">setBarycenter</A>, <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#setSize(double)">setSize</A>, <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#side(org.apache.commons.math3.geometry.partitioning.Hyperplane)">side</A></CODE></TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_java.lang.Object"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from class java.lang.<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</A></CODE></TD>
</TR>
</TABLE>
&nbsp;
<P>

<!-- ========= CONSTRUCTOR DETAIL ======== -->

<A NAME="constructor_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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<B>Constructor Detail</B></FONT></TH>
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</TABLE>

<A NAME="PolygonsSet()"><!-- --></A><H3>
PolygonsSet</H3>
<PRE>
public <B>PolygonsSet</B>()</PRE>
<DL>
<DD>Build a polygons set representing the whole real line.
<P>
</DL>
<HR>

<A NAME="PolygonsSet(org.apache.commons.math3.geometry.partitioning.BSPTree)"><!-- --></A><H3>
PolygonsSet</H3>
<PRE>
public <B>PolygonsSet</B>(<A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/BSPTree.html" title="class in org.apache.commons.math3.geometry.partitioning">BSPTree</A>&lt;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Euclidean2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Euclidean2D</A>&gt;&nbsp;tree)</PRE>
<DL>
<DD>Build a polygons set from a BSP tree.
 <p>The leaf nodes of the BSP tree <em>must</em> have a
 <code>Boolean</code> attribute representing the inside status of
 the corresponding cell (true for inside cells, false for outside
 cells). In order to avoid building too many small objects, it is
 recommended to use the predefined constants
 <code>Boolean.TRUE</code> and <code>Boolean.FALSE</code></p>
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>tree</CODE> - inside/outside BSP tree representing the region</DL>
</DL>
<HR>

<A NAME="PolygonsSet(java.util.Collection)"><!-- --></A><H3>
PolygonsSet</H3>
<PRE>
public <B>PolygonsSet</B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</A>&lt;<A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/SubHyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning">SubHyperplane</A>&lt;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Euclidean2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Euclidean2D</A>&gt;&gt;&nbsp;boundary)</PRE>
<DL>
<DD>Build a polygons set from a Boundary REPresentation (B-rep).
 <p>The boundary is provided as a collection of <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/SubHyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning"><CODE>sub-hyperplanes</CODE></A>. Each sub-hyperplane has the
 interior part of the region on its minus side and the exterior on
 its plus side.</p>
 <p>The boundary elements can be in any order, and can form
 several non-connected sets (like for example polygons with holes
 or a set of disjoint polyhedrons considered as a whole). In
 fact, the elements do not even need to be connected together
 (their topological connections are not used here). However, if the
 boundary does not really separate an inside open from an outside
 open (open having here its topological meaning), then subsequent
 calls to the <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#checkPoint(org.apache.commons.math3.geometry.Vector)"><CODE>checkPoint</CODE></A> method will not be meaningful anymore.</p>
 <p>If the boundary is empty, the region will represent the whole
 space.</p>
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>boundary</CODE> - collection of boundary elements, as a
 collection of <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/SubHyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning"><CODE>SubHyperplane</CODE></A> objects</DL>
</DL>
<HR>

<A NAME="PolygonsSet(double, double, double, double)"><!-- --></A><H3>
PolygonsSet</H3>
<PRE>
public <B>PolygonsSet</B>(double&nbsp;xMin,
                   double&nbsp;xMax,
                   double&nbsp;yMin,
                   double&nbsp;yMax)</PRE>
<DL>
<DD>Build a parallellepipedic box.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>xMin</CODE> - low bound along the x direction<DD><CODE>xMax</CODE> - high bound along the x direction<DD><CODE>yMin</CODE> - low bound along the y direction<DD><CODE>yMax</CODE> - high bound along the y direction</DL>
</DL>
<HR>

<A NAME="PolygonsSet(double, org.apache.commons.math3.geometry.euclidean.twod.Vector2D...)"><!-- --></A><H3>
PolygonsSet</H3>
<PRE>
public <B>PolygonsSet</B>(double&nbsp;hyperplaneThickness,
                   <A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Vector2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Vector2D</A>...&nbsp;vertices)</PRE>
<DL>
<DD>Build a polygon from a simple list of vertices.
 <p>The boundary is provided as a list of points considering to
 represent the vertices of a simple loop. The interior part of the
 region is on the left side of this path and the exterior is on its
 right side.</p>
 <p>This constructor does not handle polygons with a boundary
 forming several disconnected paths (such as polygons with holes).</p>
 <p>For cases where this simple constructor applies, it is expected to
 be numerically more robust than the <A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/PolygonsSet.html#PolygonsSet(java.util.Collection)"><CODE>general
 constructor</CODE></A> using <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/SubHyperplane.html" title="interface in org.apache.commons.math3.geometry.partitioning"><CODE>subhyperplanes</CODE></A>.</p>
 <p>If the list is empty, the region will represent the whole
 space.</p>
 <p>
 Polygons with thin pikes or dents are inherently difficult to handle because
 they involve lines with almost opposite directions at some vertices. Polygons
 whose vertices come from some physical measurement with noise are also
 difficult because an edge that should be straight may be broken in lots of
 different pieces with almost equal directions. In both cases, computing the
 lines intersections is not numerically robust due to the almost 0 or almost
 &pi; angle. Such cases need to carefully adjust the <code>hyperplaneThickness</code>
 parameter. A too small value would often lead to completely wrong polygons
 with large area wrongly identified as inside or outside. Large values are
 often much safer. As a rule of thumb, a value slightly below the size of the
 most accurate detail needed is a good value for the <code>hyperplaneThickness</code>
 parameter.
 </p>
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>hyperplaneThickness</CODE> - tolerance below which points are considered to
 belong to the hyperplane (which is therefore more a slab)<DD><CODE>vertices</CODE> - vertices of the simple loop boundary<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DL>

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<A NAME="buildNew(org.apache.commons.math3.geometry.partitioning.BSPTree)"><!-- --></A><H3>
buildNew</H3>
<PRE>
public <A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/PolygonsSet.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">PolygonsSet</A> <B>buildNew</B>(<A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/BSPTree.html" title="class in org.apache.commons.math3.geometry.partitioning">BSPTree</A>&lt;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Euclidean2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Euclidean2D</A>&gt;&nbsp;tree)</PRE>
<DL>
<DD>Build a region using the instance as a prototype.
 <p>This method allow to create new instances without knowing
 exactly the type of the region. It is an application of the
 prototype design pattern.</p>
 <p>The leaf nodes of the BSP tree <em>must</em> have a
 <code>Boolean</code> attribute representing the inside status of
 the corresponding cell (true for inside cells, false for outside
 cells). In order to avoid building too many small objects, it is
 recommended to use the predefined constants
 <code>Boolean.TRUE</code> and <code>Boolean.FALSE</code>. The
 tree also <em>must</em> have either null internal nodes or
 internal nodes representing the boundary as specified in the
 <A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#getTree(boolean)"><CODE>getTree</CODE></A> method).</p>
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html#buildNew(org.apache.commons.math3.geometry.partitioning.BSPTree)">buildNew</A></CODE> in interface <CODE><A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/Region.html" title="interface in org.apache.commons.math3.geometry.partitioning">Region</A>&lt;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Euclidean2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Euclidean2D</A>&gt;</CODE><DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#buildNew(org.apache.commons.math3.geometry.partitioning.BSPTree)">buildNew</A></CODE> in class <CODE><A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="class in org.apache.commons.math3.geometry.partitioning">AbstractRegion</A>&lt;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Euclidean2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Euclidean2D</A>,<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/oned/Euclidean1D.html" title="class in org.apache.commons.math3.geometry.euclidean.oned">Euclidean1D</A>&gt;</CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>tree</CODE> - inside/outside BSP tree representing the new region
<DT><B>Returns:</B><DD>the built region</DL>
</DD>
</DL>
<HR>

<A NAME="computeGeometricalProperties()"><!-- --></A><H3>
computeGeometricalProperties</H3>
<PRE>
protected void <B>computeGeometricalProperties</B>()</PRE>
<DL>
<DD>Compute some geometrical properties.
 <p>The properties to compute are the barycenter and the size.</p>
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html#computeGeometricalProperties()">computeGeometricalProperties</A></CODE> in class <CODE><A HREF="../../../../../../../org/apache/commons/math3/geometry/partitioning/AbstractRegion.html" title="class in org.apache.commons.math3.geometry.partitioning">AbstractRegion</A>&lt;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Euclidean2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Euclidean2D</A>,<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/oned/Euclidean1D.html" title="class in org.apache.commons.math3.geometry.euclidean.oned">Euclidean1D</A>&gt;</CODE></DL>
</DD>
<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="getVertices()"><!-- --></A><H3>
getVertices</H3>
<PRE>
public <A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Vector2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Vector2D</A>[][] <B>getVertices</B>()</PRE>
<DL>
<DD>Get the vertices of the polygon.
 <p>The polygon boundary can be represented as an array of loops,
 each loop being itself an array of vertices.</p>
 <p>In order to identify open loops which start and end by
 infinite edges, the open loops arrays start with a null point. In
 this case, the first non null point and the last point of the
 array do not represent real vertices, they are dummy points
 intended only to get the direction of the first and last edge. An
 open loop consisting of a single infinite line will therefore be
 represented by a three elements array with one null point
 followed by two dummy points. The open loops are always the first
 ones in the loops array.</p>
 <p>If the polygon has no boundary at all, a zero length loop
 array will be returned.</p>
 <p>All line segments in the various loops have the inside of the
 region on their left side and the outside on their right side
 when moving in the underlying line direction. This means that
 closed loops surrounding finite areas obey the direct
 trigonometric orientation.</p>
<P>
<DD><DL>

<DT><B>Returns:</B><DD>vertices of the polygon, organized as oriented boundary
 loops with the open loops first (the returned value is guaranteed
 to be non-null)</DL>
</DD>
</DL>
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